CREEP TO RUPTURE BEHAVIOR OF CONCRETE BEAMS

BY

JOHN LEONARD WALKINSHAW

Diplome E.T.S. Geneva(1967)

(Switzerland)

Submitted in partial fulfillment

of the requirements for the degree of

Master of Science in Civil Engineering

at the

Massachusetts Institute of Technology

(February,

Signature of AuthorDepartment of

Certified by ............

Accepted by .............

Civil Engineering, (January 20, 1969)

... .... .. .. .. .. .- , .. .-. g .. -. -..

Thesis Supervisor

1 Commnittee on Graduate Students

1969)

AI . A

Chairman, Departmenta

- 1 -

ABSTRACT

CREEP TO RUPTURE BEHAVIOR OF CONCRETE BEAMS

by

JOHN LEONARD WALKINSHAW

Submitted to the Department of Civil Engineering onJanuary 24, 1969 in partial fulfillment of the requirementsfor the degree of Master of Science in Civil Engineering.

A laboratory technique utilizing cast notched beamsof cement paste, mortar and concrete was used to study therole of solid inclusions in the bending behavior ofconcrete. To determine the properties of the individualmixes, a series of conventional tests were made. Thefracture parameters of the mixes were calculated. The longterm behavior of the beams under loads approaching theultimate was then established.

The results of this study show that most of thecharacteristics of the material improve when aggregate ispresent in the mix. In long term loading the service lifeof the beams increased with decreasing loads. At comparableultimate load fractions (load levels) the creep rates wereapproximately the same. There was an apparent linear rela-tionship (on semi log scale) between the maximum time tofailure and the load levels tested. All three mixes showedlower stiffness after being subjected to load than if noload had been applied over the same period of time.

For the series of beams tested the long term ultimatestrength was .80 of the short time static strength.

Thesis Supervisor: Fred Moavenzadeh

Title: Associate Professor of Civil Engineering

-2 -

ACKNOWLEDGMENTS

The author wishes to thank Dr. Fred Moavenzadeh,

thesis supervisor, for his careful review and positive

suggestions during the preparation of this thesis. He

further wants to acknowledge Mr. Arthur Rudolph for his

help in the design and manufacture of the equipment and

Mr. Ted Bremner for his valuable advice on certain sections

of this thesis. Final thanks are extended to my other

colleagues for their constant support throughout the

project and to my wife for her patience and her typing of

the drafts.

-3-

CONTENTS

Page

Title Page.......................................... 1

Abstract....................................................................... 2

Acknowledgments............. .................. 3

Table of Contents ................................... 4

List of Figures .................... .................

List of Tables............................. ........... 7

Body of Text............ ........................... 8

I. Introduction............................. 8

II. Review of Literature ...................... 10

General Considerations of Creepto Rupture.............................. 10

III. Materials and Procedure .................. 24

Materials................. ......... 24

Specimen Size.......................... 28

Design of Mixes ...... .............. ..... 31

Fabrication and Curing...............

Testing Equipment and TestingProcedure....... . ....................... 33

Static Tests ..................... .... 33Creep to Rupture Tests................ 33

IV. Results and Discussion of Results........ 39

Conventional Tests..................... 39

Modulus of Rupture.................... 39Modulus of Elasticity ................. 43Compressive Strength................. 50

Calculation of Fracture MechanicsParameters.............................. 52

-4-

CONTENTS

(continued)

Page

Creep to Rupture Tests............

Creep Rates.....................Magnitude of Creep...............Tertiary Creep..................Deflections at Failure..........Effects of Static Fatigue onShort Time Tests................

V. Conclusions ..........................

List of References .............. ... .......... .

Appendices ......................................

A. List of Abbreviations in Text.......

B. List of Deflections Recorded in theCreep to Rupture Curves.............

5758626364

65

76

78

83

83

...

... 85

-5-

LIST OF FIGURES

Title Page

1 Schematic Creep Curve ........................

2 Beam Geometry................... .............

3 Geometry of the Removable Brass Notch........

4 Instron Testing Machine with Beam Set-up.....

5 Creep to Rupture Loading Device withRecorder................... ...... ,, .. .......

6 Creep to Rupture Loading Device with Clocka) Schematic Representation...............b) Actual Set-up.........,................

7 Typical Load-Deflection Curves Representinga) Catastrophic, b) Semi-Stable, c) StableFracture .....................................

8 Strain Measurement on Tension Side of Beamsin Flexure

a) Position of Strain Gage Pins..........b) Positioning of Mechanical Strain Gage..

9 Stress-Strain Curves from Measurements onTension Side of Beams in Flexure.............

10 Stress-Strain Curves from Measurements on2"x 4'" Cylinders in Compression ..............

11 CreepPaste

12 Creep

13 Creep

14 SummaLevelTest.

15 Summavs. T:

to Rupture........to Rupture

to Rupture

to Rupture

ry of Testsvs. Time t

.. . .....

ry of Testsime to Rupt

Recordings for Cement

Recordings for Mortar........

Recordings for Concrete.....

for Cement Paste. Loado Rupture or Duration of............................ .

for Mortar. Load Levelure or Duration of Test......

5960

61

72

7316 Summary of Tests for Concrete. Load Level

vs. Time to Rupture or Duration of Test .....

-6-

FigureNumber

LIST OF TABLES

TableNumber Title Page

1 Results of Conventional Tests on theAggregates.................................. 25

2 Gradation of Aggregates...................... 26

3 Manufacturer's Laboratory Report on thePortland Cement............................. 27

4 Mix Proportions.......... ..................... 32

5 Modulus of Rupture in Flexure (7 day &28 day)....................................... 40

6 Modulus of Elasticity (7 day & 28 day)Determined from Flexure Tests..,....,....... 44

7 Modulus of Elasticity (28 day & 140 day)and Compressive Strength Determined on2"x4" Cylinders. Compressive Strength(28 day) of 2" Cubes .............,,........... 51

8 Fracture Mechanic Parameters for CementPaste, Mortar and Concrete (28 day tests)... 55

9 Cement Paste Beams Tested in Creep toRupture Device with Clock.................... 67

10 Mortar Beams Tested in Creep to RuptureDevice with Clock........................... 68

11 Concrete Beams Tested in Creep to RuptureDevice with Clock .............,........... 69

I. INTRODUCTION

Concrete when subjected to sustained loading has

exhibited creep phenomenon. This phenomenon has long been

recognized by structural engineers and several methods are

suggested in the literature to account for creep behavior

of concrete in the design of structural elements. The

materials engineers on the other hand have been concerned

with the understanding of the creep mechanism of concrete

and have attempted to control the creep ratio through

control of concrete proportion and quality of its constitu-

ents.

The creep behavior of concrete has mostly been consid-

ered at low levels of stresses and little is known about

the behavior of concrete under sustained load levels close

to its short time ultimate strength. This behavior which

in other materials is referred to as static fatigue or

creep to rupture is not only of interest in the design of

structures but is also useful in the understanding of the

behavior of material.

It is therefore the purpose of this thesis to obtain

better understanding of the behavior of concrete in bending

at load levels approaching the short time ultimate

strength.

-8-

To study the influence of the different constituents

of the concrete, cement, mortar and concrete beams were

made. Fracture mechanics parameters were determined ex-

perimentally for each mix to explain what role solid inclu-

sions play in the strengthening and toughening of concrete

when subjected to the above loading conditions. Since

failure occurs at the high levels of testing loads, rela-

tionships between load levels and time to failure were

recorded. From these recordings the long term ultimate

strength was determined and compared to that found in the

literature for compressive strengths of the materials,

-9-

II. REVIEW OF LITERATURE

A review of the literature on creep and creep rupture

of structural materials is presented in this section. The

creep process and its basic causes in various materials are

discussed in the hope that the progress made in other

materials can be of use in the study of the behavior of

concrete.

General Considerations of Creep to Rupture

In design for creep the most important properties used

are creep strength and creep rupture strength. The American

Society for Testing and Materials (ASTM) defines these

properties as the highest stresses that a material can

stand for a specified length of time without excessive de-

formation or rupture respectively [11*.

As opposed to a cyclic fatigue test [2], which deter-

mines the number of cycles a material can safely endure over

a certain stress range in an environment3 a creep to rupture

test [3] determines the service life under constant load or

stress in the environment of application.

* Numbers in [ ] refer to references.

- 10 -

There are two principal methods for predicting creep

strength:

1. Several specimens are tested simultaneously

at different stresses and at the expected

operating temperature. Time to reach the

allowable strain is recorded for each spec-

imen and a plot of stress vs. time can be

drawn. From this plot, the service life of

a specimen can be determined knowing the

stress and temperature during operation.

2. The second method is based on the creep

rate of the secondary (steady) creep.

Knowing the allowable strain E , the

elastic strain E , and the service life.0

tj , these can be combined to give an

allowable minimum creep rate

E1 - E o

V = oo tt

1

This assumes transient creep to be completed

and represents a schematic creep curve

(Figure 1).

Each test is performed at different stress until the mini-

mum creep rate appears to be well established. The results

are plotted with V as a function of stress.

The creep to rupture concept is applied mostly to

metals and polymers which have been playing an increasing

role in modern technology. For example space technology

and precision work require the exact knowledge of the mate-

rial's behavior under increasingly high stresses and

- 11 -

(A)

t , Time

Instantaneous DeformationTransient or Primary CreepSecondary CreepTertiary CreepFailure of Specimen

V Creep Rateo

Figure 1. Schematic Creep Curve

- 12 -

E0

---

- -

temperatures. For metallic materials the time-dependent

deformation and rupture characteristics become of primary

concern at temperatures in excess of one-half of their

absolute melting temperatures (.5 TM),

But in many new alloys the amount of creep deformation

may not be the only factor governing service lifetime.

Some have been found to fracture after very limited defor.

mation, so time to rupture may be shorter than the time to

reach a critical strain [4]. To understand the mechanisms

of creep in these materials it is necessary to take a look

at their microscopic structure.

The grain size in metallic materials has been shown to

have a moderate effect on steady state creep [5,6]. In

general, the creep rate decreases with increasing grain

size, but in coarse grained materials (2r > 0.1 mm) the

reverse can be true. But the grain boundaries transverse

to the applied stress tend to be sites for void nucleation.

This mechanism and energy considerations of fracture by

vacancy creep are reviewed in detail by Cottrell [7].

Metallic materials also work-harden in the process of

deformation and thus the creep rate results from a balance

of simultaneous work-hardening and recovery processes. In

the individual crystals two significant stress aided and

thermally activated recovery processes exist. These are

- 13 -

cross-slip and dislocation climb [8,9] which both act

primarily at different temperatures.

At low temperatures cross-slip prevails and is the

movement of screw dislocations around obstacles. Recovery

at high temperatures (above .5 TM) is done by dislocation

climb. Climb is controlled by the rate of diffusion of

vacancies to or from dislocation jogs under the action of

the local stress fields.

Another method to reduce creep in metals is to alloy

them with suitable elements. This raises the temperature

of recrystallization and produces precipitants along the

grain boundaries which reduces dislocation movements.

Other mechanisms are also involved in creep of metallic

materials. However it is not the scope of this review to

go into further detail but to present a few mechanisms that

are somewhat similar to those found in concrete.

In polymeric materials the trends are also similar to

those of concrete and metallic materials. Many polymers

exhibit fatigue or endurance limits in their stress vs.

number of cycles (S-N) curves. The fatigue limit is often

between 20% and 35% of the static tensile strength.

The fatigue life of a polymer is generally reduced by

an increase in temperature. For example, the fatigue life

of poly methyl methacylate (PMMA) decreases by 58% in going

- 14 -

from -300F to 800F [10]. These temperatures are below its

glass transition temperature (900F).

With the increasing wide use of polymers in everyday

objects (plastic raincoats to rubber tires) it was found

necessary to investigate the material properties under

constant load (raincoat hanging on a hook, car in parking).

The creep mechanics in polymers for the steady state

creep is viscous flow of the polymer chains around each

other. A study done at Massachusetts Institute of Tech-

nology [11] on PMMA in creep to rupture shows that the

stress limit (at 10000 hrs) is 35% of the short term (10

sec) static stress at room temperature. This limit varied

with varying surface treatments, temperature and preheating

of the specimens before testing.

The addition of fillers or glass fibers to the poly-

mers increased the creep resistance by increasing the vis-

cosity or basically following the same principles applied

to metallic materials.

These trends of varying testing conditions are

generally valid for the majority of the polymers and are

widely covered in the literature and many references to

them can be found in the books by Nielson [12] and Baer

[13].

As for the work on concrete, it has been widely

covered throughout this century.

- 15 -

Because of the wide variety of constituents entering

a concrete mix it is often difficult to make definite

comparisons, but general trends have been established and

are well known. Most of the work has been done in either

cyclic fatigue or creep at low levels of stress.

The cyclic fatigue testing simulates the loading of a

wide variety of concrete structures the most important of

which are bridges. Most studies have been done in com-

pression and flexure although tests in tension and torsion

are also reported.

The S-N (stress vs. number of cycles) curve for

concrete does not exhibit a fatigue limit but continues to

drop as N increases. For a large number of cycles

(2 x 106), the cyclic fatigue strength in compression is

approximately 50% to 60% of the short static strength. In

flexural tension stress in nonreinforced beams, the

"fatigue limit"' has been reported [14] to be 55% for

2 x 106 cycles and between 40% to 66% of static strength

for 107 cycles [15]. The mechanisms of failure occurring

during the cyclic testing have been found to be strongly

related to the following four parameters:

1. The presence of stress regardless of

origin or time variation.

2. The repeating nature of some stresses.

- 16 -

3. The presence of discontinuities such as

microcracks, macrocracks and structural

heterogeneity.

4. The resistance of concrete to failure.

This last parameter has been defined by the following

mechanism.

The internal flaws in a concrete specimen are large

compared to the gel structure of the matrix. These flaws

act as stress raisers. The average stress across the

cross-section is much smaller than the stress at crack tips

(Griffith theory). Microcracks relieve the stress at the

tip of the macrocracks by the formation of new surfaces

(expended surface energy) and the ability of the micro-

cracks to stabilize macrocracks in a stress field is the

resistance of concrete to failure.

The repeating stresses in cyclic fatigue modify the

formation of microcracks and cause a slow, stable growth of

macrocracks until the unstable condition is reached.

The other widely performed experiment is creep of

concrete under constant stress. As seen previously in

metals and other crystalline materials, creep is attributed

to slip in crystals. While slip of this nature undoubtedly

occurs [17] in aggregate particles and within crystalline

particles that are part of hydrated paste, there is ample

evidence that they are only secondary factors in creep of

- 17 -

concrete. Crystalline slip is normally detectable only

above some threshold level of stress.

Creep of concrete has been observed at all stresses as

low as 1% of ultimate [18]. It has been explained by many

mechanisms of which the following or any combination of them

are the most important:

1. Seepage of colloidal (absorbed) water from

the gel formed by hydration of cement [19,20].

2. The effect of shrinkage [21,22].

3. The accessibility to water of the large

internal surface of the gel structure [17].

4. Delayed elasticity [23].

5. Opening or closing of internal voids.

6. Intercrystalline deformation.

Some evidence supporting the first three mechanisms is that

no creep was observed in tests made on dried pastes [24].

Creep of concrete is a linear function of stress up to

20% to 25% [25] or 35% to 40% of ultimate [17] depending on

the authors. In either case this is in the normal working

range of concrete in structures. A wide variety of

research has been performed on creep in this range,

studying the different behaviors and factors influencing

such behaviors of plain and reinforced concrete. A fairly

complete review on laboratory and field tests covering the

years 1905-1956 can be found in Reference [26].

- 18 -

More recently creep behavior has been studied with the

help of models. This enables researchers to formulate

mathematical theories in the prediction of concrete defor-

mation under load [25,27,28].

These models supplemented by laboratory tests allow

also the computation of deformations of structures subjected

to variable stress from results under constant stress [29].

Reference [29] explains three methods for doing this analy-

sis. Each one of the three methods has a certain advantage

in particular circumstances depending on the stress varia-

tion, the extent of creep data available and the accuracy

desired.

Although most of the creep tests are performed in com-

pression, some studies have been made in tension [26]. In

tension, the rate of creep is greater in the first few

weeks than in compression when reduced to 1 psi. Later the

reverse is true but the ultimate is approximately the same.

This finding stimulated the researchers to study creep in

bending.

Their report on bending of nonreinforced beams sub-

jected to a constant bending moment showed that the early

creep of the fiber in the tension side was also greater

than the corresponding creep of the compression side.

Apart from these tests conducted at the normal working

loads some researchers have studied the effects of higher

- 19 -

stress magnitudes.

The tendency to part from the exact proportionality

increases as the values of the sustained stress increase

[30]. Sustained stress above normal working stress pro-

duces creep that increases at progressively faster rate, as

the magnitude of sustained stress is increased. Glanville

and Thomas [31] proposed that a master curve could be

obtained, for stresses up to 84%, by multiplying the strain

at each load level by respective constants. These constants

decreased with increasing load level (master curve at 84%

of ultimate). They therefore concluded that "the mechanism

of large deformations as failure is approached is the same

as that of the creep at working stresses". This is stated

to be false by many other researchers because generally

failure has been recorded at lower stress levels than the

ones quoted above. It is generally agreed that the ulti-

mate strength under sustained loads determined on prismat-

ical specimens is about 70% to 75% of the short time ulti-

mate cube strength [14,32,33]. The performance of the

concrete at this stress level is basically different from

creep.

In the last ten years, the increasing interest in the

actual fracture process of concrete has lead researchers to

investigate these high levels of stress, Usually these

tests are of short duration and involve a substantial

- 20 -

amount of electronic equipment.

Leslie and Cheesman [34] in measurements of the

variance of the sonic velocity in a specimen noticed a

marked decrease in it when the load approached 75% of the

utlimate. Shah and Chandra [35] measured an increase in

Poisson's ratio accompanied by an increase of cracking

noises at the same load level as in [34]. These cracking

noises were also observed in experiments by Rusch [36].

The detection of these cracking noises was first made at

load levels between 30% and 50% of the ultimate and were

intermittent up to 70% to 75% at which point they increased

substantially.

Visual detection of the cracking in concrete was also

undertaken by several researchers. Hsu [52] used a tech-

nique of first loading a small cylinder to a certain load

level, unloading it, slicing it in thin sections, then ink

staining the surface for visual observation of the crack

patterns under a microscope. The first increase of bond

cracks was observed at load levels above 30% of the ulti-

mate and occurred around the larger aggregate (weaker bond

strength). As the loading increased so did the number of

cracks until they formed continuous crack patterns at 70%

to 90% of the ultimate. This corresponds well with the

findings using the sonic methods and accounts for the

increase of Poisson's ratio. Hansen [33] used a different

- 21 -

technique, in as much as he cut slabs from prismatical

specimens before drying and testing them. The specimens

were loaded to certain levels and kept under constant

stress until crack propagation had stabilized (4 days).

The stress was then increased to a higher level and main-

tained again, and this process continued up to failure.

The observance of the crack propagation could be made

directly and it was reported that never more than two

cracks caused failure.

This type of testing simulates more accurately the

type of loading (long term) a structural member may undergo

and the observed cracking is less likely to be due to ex-

perimental procedure (machining).

Another method of showing the cracking of concrete at

high levels was presented by Glucklich [53] in 1959. Two

series of specimens were tested, one in a normal "hard"T

machine and the second with the interpositioning of a

spring between the specimen and the crosshead to make a

"soft" machine. The specimens tested in the "soft" machine

all failed at lower loads than in the "hard" machine.

The essential difference between the two types of

loading consists in stored energy considerations. In the

"soft" machine there is a practically unlimited store of

elastic energy available whereas in the "hard" machine the

- 22 -

only energy available is stored in the specimen. As seen

previously, the mechanism of fracture of the material, in

a "hard" machine, is such that local fracture isusually

arrested soon after it starts spreading because its energy

supply is exhausted. In the "soft" machine, when crack

growth was checked by a region of low energy, the spring

contributed an additional supply of energy to overcome the

obstacle and produced earlier failure of the specimen.

This method of testing in a "soft" machine is nearly

the equivalent of testing a specimen to failure by

providing constant stress and Glucklich's conclusions were:

"Concrete is sensitive to static fatigue, The conclusion

is therefore that in strictly sustained loads or in

statically determinate systems, the time effect on strength

can lead to total failure at loads below the normal

breaking loads......"

Therefore the failure load of concrete could be

defined as the load at which fast crack propagation begins.

In the next sections it will be explained how, in this

study, the failure loads were determined for cement paste,

mortar and concrete beams in bending. Fracture mechanics

parameters and other material properties will also be dis-

cussed.

- 23 -

III. MATERIALS AND PROCEDURE

In this section the materials and the test procedures

used to determine the results are discussed,

Materials

The sand and gravel (pea stone) used in the different

mixes were obtained from a local supplier. The conven-

tional tests and gradation results are presented in Tables

1 and 2.

The aggregates were oven dried and stored in

- containers in the laboratory. After the first gradation

tests, it was decided to exclude the sand retained on the

Number 4 sieve (approximately 6%) to correspond more

accurately to the Bureau of Reclamation Specifications

[401. Also the gravel retained on the 3/8" sieve (approxi-

mately 24%) was excluded because of the maximum size re-

strictions [41] for the specimen geometry described later.

The cement used was Type 1 Portland Cement. The manu-

facturer's laboratory report for this cement is shown in

Table 3.

- 24 -

Table 1

Results of Conventional Tests on the Aggregates

Origin: uncrushed extracted from piles

Sand:

Specific Gravity SSD

Unit Weight (oven dry)

Moisture Content SSD

Fineness Modulus

Maximum Size

2.63

111 lb/ft3 (1.78 g/cm3 )

1%

2.75

.187 in (0.45 cm)

Gravel:

Specific Gravity SSD

Unit Weight (oven dry)

Moisture Content SSD

Fineness Modulus

Maximum Size

2.67

96 lb/ft3 (1.54 g/cm3 )

1%

5.60

.375 in (0.95 cm)

- 25 -

Tab le 2

Gradation of Aggregates

Sand:

% rounded to nearest whole number

Sieve Size Retained on Cumulative Bureau ofSieve (% by (% by weight) Reclamationweight) Specification

No.4 0 0 0- 5

8 16 16 10-20

16 17 33 20-40

30 19 52 40-70

50 27 79 70-88

100 16 95 92-98

275

Fineness Modulus 275/100 = 2.75

Gravel: (pea stone)

Sieve Size Retained on CumulativeSieve

3/8" 0 01/4" 71 71

No.8 22 93

16 6 9930 99

50 99100 99

560

Fineness Modulus 560/100 = 5.60

- 26 -

Table 3

Manufacturer's Laboratory Report

on the Portland Cement

Specification and Type: Type I Bag

CHEMICAL

SiO 2 .................

CaO ..................

Mg0 ..................

SO ...................

Ignition Loss ........

Insoluble Residue ....

Potential CompoundsTricalcium SilicateTricalcium Aluminate

PHYSICAL

Wagner ......................

Blaine ........ ..............

Autoclave Expansion .........

Time of Setting, GillmoreInitial (hr:min) ..........Final (hr:min) ...........

Compressive Strength, psi1-day .... .. ...............3-day .................. .....7-day .....................28-day .....................

Air Entrainment, % by volume

..... 99.............a e.O961QIQ e 0 4 e1

.. 9

- 27 -

20.39%

6.20%2.69%

63.36%

3.20%2.22%

0.36%

0.09%

51.09%11.88%

1962

33210.431%

3:135:02

17003500488057689.3%

. ao ef e ee e a .

eooeleoeleeee.

Specimen Size

A notched beam subjected to three point bending was

selected as the type of specimen for use in this study of

creep to rupture of concrete for several reasons. Notching

of the specimen on the tension side creates a high stress

concentration on a relatively small region. The location

of fracture initiation is thereby controlled. It also

reduces the scatter in the ultimate load bearing capacity.

Testing the concrete in a tensile fashion focuses on the

weakest and the microscopically most likely mode of

fracture.

The nominal dimensions of all the beams were

2" x 2" x 22". All the specimens had notches such that the

ratio of notch depth to overall depth a/d was .375 (see

Figure 2).

The notch geometry was designed for easy removal of

the beam from the mold (see Figure 3). The notch could be

removed from the mold partitions if unnotched beams were

desired. The notches were situated at the midspan on the

tensile faces of the specimen and were made of brass.

Design of Mixes

Trial mixes were made to determine the best water-

cement ratio (W/c) and aggregate-cement ratio (A/c) to

- 28 -

L

- S

Notch Depth

Beam Depth

Beam Width

OverallLength

Span

a/d = .375

S/d = 10

a = .75"

d = 2"

w = 2"

L = 22"

S = 20"

Figure 2. Beam Geometry

- 29 -

Figure 3. Geometry of the Removable Brass Notch

- 30 -

obtain workable mixes. It was felt that an A/c ratio

lower than 3.0 would not be representative of a practical

mix. Also the W/c ratio of .4 was found to be the maxi-

mum ratio that could be used in cement paste without exces-

sive bleeding. Higher A/c ratios than 3.0 were tried but

the mixes could not be satisfactorily molded.

The proportions by weight of the final mixes are

presented in Table 4. The weights of the aggregates are

given in the saturated surface dry (SSD) condition.

Fabrication and Curing

Each batch (approximately 100 lbs) was prepared to

make twelve beams cast into two plexiglass molds. The

molds and notches were oiled prior to each pouring.

The aggregate, water and cement were preweighed taking

into account that the aggregate was not in SSD condition.

A one cubic foot capacity concrete mixer was used and

mixing was continued for five to six minutes after all the

mix constituents had been added. The mix was then poured

in the molds in three layers and the vibrating table on

which the mold was resting was activated two to three

minutes for each layer put in.

Following the casting of the twelve beams the molds

were covered under polystyrene sheeting. Saturated sponges

- 31 -

Table 4

Mix Proportions

Cement Paste Mortar f onc're te

water/cement .4 .4 4

sand/cement 3.0 1.2

gravel/cement 1.8

aggregate/cement 3.0 3.0

ug/cm3 2.04 2.34 2.43unit weight

lb/ft 3 128 146 152

cement contentbags/yd3 26 10 10

- 32 -

were placed under the sheeting to insure a high humidity

curing prior to demolding.

The beams were demolded after twenty-four hours,

numbered, dated and cured in water until testing at twenty-

eight days.

Testing Equipment and Testing Procedure

Static Tests: The static tests were performed on an

Instron Universal Testing Machine. The load cell used had

a maximum capacity of 10000 lbs and the span of the beam

was 20 in. This testing arrangement can be seen in Figure

4. Initially, certain standard flexure tests had to be

performed on the three mixes before the creep to rupture

testing could begin. To determine the crosshead rate which

would meet the ASTM standards [42], twenty-four beams were

cast of each mix, half of which were unnotched. These beams

were tested at both seven days and twenty-eight days at two

different crosshead rates. It was found that the rate of

.005 in/min could be used and it is at this rate that all

the subsequent ultimate load determinations were made.

Creep to Rupture Tests: In this study two types of

loading devices were used for the long term loading of the

notched beams. In the first device, shown in Figure 5, it

was possible to record the deflection of the beam by means

- 33 -

Figure 4. Instron Testing Machine with Beam Set-up

- 34 -

Figure 5. Creep to Rupture Loading Device with Recorder

- 35 -

of an LVDT Transducer. The full scale on the chart paper

(100 divisions) was calibrated to be .02 in. The recorder

had two chart speeds: 1 in/min used in the first minutes of

the test and 2 in/hr used until the end of the test. In

tests of expected short duration the recorder was left on

1 in/min.

The other loading device is shown in Figures 6a and

6b. Six of these devices were made so that a total of

seven beams could be tested at one time. In this second

loading device the load is applied through a steel lever

bar at each test position. The weight is applied at the

end of the bar. The lever arm distances were such as to

apply the load at the midpoint of the test specimen of

twice the suspended weight. The weight of the bar was

included in the applied load.

The timing at each loading position was accomplished

with an electric calendar clock connected to a microswitch.

Failure of the specimen released the lever arm and opened

the microswitch, thereby stopping the clock. The time of

day in which a failure occurred could be determined by

advancing the hands of the clock to the next "1 2 o'clock"

position and seeing if the calendar date changed.

- 36 -

calendar clock

microswitch5/8p" steel loading bar

polystyrene shbettfor tank p/2

p/2

Figure 6. Creep to Rupture Loading Device with Clock

a) Schematic Representation

CA)

b. Actual Set-up

Figure 6. Creep to Rupture Loading Device with Clock

- 38 -

IV. RESULTS AND DISCUSSION OF RESULTS

In the first part of this section the results of the

conventional tests, such as modulus of rupture, modulus of

elasticity ano compressive strength, performed on the

three mixes are discussed.

In the second part the fracture mechanics parameters

(critical stress intensity factor Kc , critical strain

energy release rate G and the surface energy Y ) arec

determined from tests on the notched beams for each mix.

.In the final part of this section the results of the

creep to rupture tests are discussed and compared with the

trends noted in the other tests for paste, mortar and

concrete.

Conventional Tests

Modulus of Rupture: The first property determined for

each mix from the unnotched beams was the modulus of

rupture [42]. The values computed for seven day and

twenty-eight day tests are presented in Table 5. These

values compare well with values presented by Walker and

Bloem [441] if their values (in graph form) are extrapolated

- 39 -

Table 5

Modulus of Rupture in Flexure

(7 days & 28 days)

Age at Testing

Loading Rate (in/min)

Paste

7 days

0.002

1050 1085 975-14%+19% -8%+10% ±24%

Mortar

Concrete

910±7%

765±10%

results in psi

- 40 -

28 days

0.005 0.002 0.005

1155±15%

1070±4%

935±2%

920±3%

82010o%

985

840±12%

- --

for the richness* of mixes used in this study (Table 4).

Certain trends are noticeable in these results such

as a decrease in the flexural strength with the change in

aggregate size from mortar to concrete [54]. This can be

explained by calculations of the characteristic flaw sizes

of each mix [51]. They were shown to increase in size in

the same proportion as the maximum aggregate size. The

calculations were based on the assumption that the cracks

were "penny shaped" in an infinite body subjected to

uniform tension. Although this assumption is not exact for

bending, the values calculated give a good explanation for

the decrease in strength with increase of aggregate size,

Another trend is the general increase of strength with

increase of strain rate which is characteristic of concrete

mixes and is well documented in the literature [20,42].

It was also noted during the testing of the beams that

each mix had a characteristic mode of failure, especially

noticeable on the notched beams (see Figure 7).

Cement paste was characterized by sudden catastrophic

failure known as "unstable" fracture. This means that the

energy stored in the specimen while loading (area under the

curve) is in excess of that necessary to propagate a

* See section on "Design of Mixes".

- 41 -

100

80

60

40

20

TIME OR DEFLECTION

Figure 7. Typical Load-Deflection Curves Representing(A) Catastrophic, (B) Semi-Stable, (C) StableFracture

.01 or 2 Min.

starting crack through the specimen. Once started, the

crack propagates rapidly through the notched cross-section,

leading to complete failure of the beam in a fraction of a

second.

The failure of the mortar beams was what is known as

"semi-stable" fracture. In this mode of fracture the

energy stored in the specimen was not quite sufficient to

drive the crack through the specimen. More energy had to

be added to completely separate the two sections.

The third mode, represented by concrete, is "stable"

fracture which means that the input of energy had to be

increased continually to propagate the slow moving crack

through the specimen cross-section. It is interesting to

note the energy required to fracture the specimens

increases with the increase of aggregate size (mortar vs.

concrete), and this will be referred to in more detail in

the "Fracture Mechanics Parameters" section.

Modulus of Elasticity: Values of the modulus of

elasticity E were necessary to calculate the fracture

mechanics parameters of the mixe~ used in this study.

These values were first determined using the load-deforma-

tion curves obtained from flexure tests. These results

are presented in Table 6. Since the values obtained in

this manner are lower than expected for these types of

- 43 -

Table 6

Modulus of Elasticity

Determined from Flexure Tests

(7 days & 28 days)

Modulus E x 106 psi

Age at Testing

Loading Rate (in/min)

7 days

0 .002,

28 days

.0.00.5. ..0.0.02 . .0 ,005

Paste .938 1,100 1.063 1.230

Mortar .1.450 1.225 1.250 1.620

Concrete 1.340 1,440 1.375 1.675

Modulus of elasticity E determined from

_ 1 PS3

-•U EI-

where 6 = maximum deflection of beams

P = maximum load

S = span of beam tested

E = modulus of elasticity of the material

I = moment of inertia of beam cross-section

- 144 -

mix [19]*, two other methods were used to determine E

using mechan:cal strain gages. The first measurements were

taken on the tension side of unnotched beams as shown in

Figure 8a and 8b. Later, the same type of measurements

were taken at one-hundred-fifty-four days on halved

sections of notched beams (11 in) on a 10 in span. The

results are plotted as stress-strain curves ,;ith the

stress calculated at the level of the center of the gage

point. Each curve presented in Figure 9 is the average

of three tests, and show the same trends as those presented

in [55].

The second measurements with the strain gage were

performed on standard 2" x 4" cylinders tested in

compression [43]. The strain values were recorded on

opposite sides of the cylinders and were averaged for each

stress level. The tests were performed at twenty-eight

and one-hundred-forty days. The stress-strain curves

presented in Figure 10 are the average of four measurements

obtained on two cylinders. The values of the computed

moduli and associated compressive strengths are presented

* Later measurements showed that 45% to 55% of totaldeformation was being absorbed in the supports. As nodefinite correcting factors could be calculated foreach mix, the values of Table 6 are not modified,

- 45 -

a. Position of Strain Gage Pins

Figure 8. Strain Measurement on Tension Side

of Beams in Flexure

- 46 -

b. Positioning

1 Division:

of Mechanical Strain Gage

strain of 2.49 x 10- s

Figure 8. Strain Measurement on Tension Side

of Beams in Flexure

- 47 -

1000

800

600

400

200

O

IO STRAINxlO5

Figure 9. Stress-Strain Curves for Measurementson Tension Side of Beams in Flexure.

15 20 30

40

OM0

x 30

w

20

10

0 10 20 30 40 50 60 70 S TRAI Nx 10 5

Figure 10. Stress-Strain Curvesfrom lMeasurementson 2" x 4" Cylinders in Compression

I

in Table 7. This table also contains the comoressive

strengths of 2 in cubes tested at twenty-eight days.

As can be noted, discrepancies exist in the values of

modulus of elasticity arrived at by the different methods

of testing. Moduli as determined in compression were

chosen to be used in calculation of fracture mechanics

parameters for the following reasons:

1. The results of flexural tests were not

accurate (see footnote, previous page).

2. The curvature of the stress-strain curves

determined on the tension face of the

beams, made it impractical to decide at

which stress level E would be

representative of each mix. This

curvature was also noted in similar

experiments by Welch [551.

The moduli as determined in compression correspond

well with the results in References [44,45] for the aggre-

gate size used and show the general trend of increase of

E with increasing aggregate size. The presence or

absence of aggregate (mortar vs. paste) appears to produce

a greater change in modulus than a small change in aggre-

gate size (mortar vs. concrete).

Compressive Strength: The third property determined

was the compressive strength, from 2" x 4" cylinders and

2 in cubes. These values are presented in Table 7 and are

- 50 -

Table 7

Modulus of Elasticity and Compressive Strength

Determined on 21' x 4"' Cylinders

(28 days and 140 days)

and

Compressive Strength of 2" Cubes

(28 days)

Age at Testing 28 days 140 days

Modulus E(psi)

CompressiveStrength

(nsi)

Modulus E(psi)

CompressiveStrength

(nsi)

Paste 2.68 x 106 7650 ± 4% 3.04 x 106 7100 + 25%- 32%

Mortar 3.97 x 106 6400 + 6.5% 4.75 x 106 7500 + 15%-15% - 17%

Concrete 4.45 x 106 7100 + 11% 4.80 x 106 6540 + 19%- 14% - 15%

Secant modulus of elasticity calculated from thestrain recorded at 2400 psi stress level.

The cylinders were capped at both ends with quickdrying plaster of paris.

Paste Mortar Concrete

CompressiveStrength

(psi) 7200 + 4% 7700 14% 8300 8 4%-- 114% 830±-4

- 51 -

for tests at twenty-eight days and one-hundred-forty days

on the cylinders and only twenty-eight days for the cubes.

As it can be noted the general values are within the

expected range for these types of mixes (10 bags/yd3 ).

No particular trend could be noted on the strengths of

the cylinders, most likely because the values are taken

from the same cylinders from which the moduli E were

calculated. The measurements of E required cycling of

the load a few times which may have reduced the strengths

somewhat. However the testing of the 2 in cubes showed a

general increase of strength with the increase of size of

aggregate which is what is to be expected for this range of

aggregate and specimen size [44].

Calculation of Fracture Mechanics Parameters

During the preliminary test of notched and unnotched

beams (see "'Testing Procedure") a series of the materials

properties were determined. From the notched beams, the

critical stress intensity facto2 Kc ,the critical strain

energy release rate GC , and the surface energy Y were

calculated using the following relations.

* The applicability of these relations to concrete arediscussed in detail in Reference [46].

- 52 -

The expression for determining Kc was taken from

Reference [P7] and is

K =Y al/2c wd2

where: a = notch depth,

d = beam depth,

w = beam width,

M = applied bending moment,

Y = f(a/d) constant = 2.08.

This expression is very similar to that used by

Lott and Kesler [48] in their study on fracture of

concrete. The only difference is the value of the constant

which changes the values by 6%.

Having calculated Kc , the values of G can be

determined using Irwin's [49] expression for brittle

fracture of materials

TrK 2G - cc E

where: E = modulus of elasticity of thematerial,

Subsequently YG can be determined from the expression

GY cG 2

where: YG = specific surface energy from

- 53 -

Irwin's expression, andspecific surface energy =energy to fracture a specimen/totalarea of new surfaces created.

Another method for determining the surface energy Y [50]

is based on the assumption that the energy expended to

induce a stable fracture is equal to the surface energy of

the newly formed surfaces. A measure of the energy input

to fracture a beam is the area under the load-deflection

curve. This is called the effective surface energy Yeff

if it is reduced to the energy required to break a unit

cross-sectional area and is expressed as the following.

U

Yeff 2A

where: U = measured input energy,

A = surface area of cross-section,

Y = effective surface energy per unitarea.

The values of these fracture parameters for cement

paste, mortar and concrete are shown in Table 8. Each one

is an average of three beams tested. The differences

--observed between the two measured surface energies YG and

Yeff are due to the following causes:

1. Cement paste beams fail unstably (see Figure

7); therefore, the measured input energy U

is in excess of that needed to fracture the

- 54 -

Table 8

Fracture Mechanics Parameters

for Cement Paste , Mortar and 'Concre te

(28 days)

k YG Yeff

lb * in- 2 in * lb/in2 in * lb/in2

Paste 357 0.075 0.084

Mortar 540 0.115 0.367Concrete 516 0.094 0.386

Loading Rate = 0.002 in/min

k c YG efflb * in - in * lb/in 2 in * lb/in2

Paste 368 0.080 0.104

Mortar 550 0.108 0,388

Concrete 610 0.131 ..... 0.588

Loading Rate = 0.005 in/min

k = critical stress intensity factor

YG = skc2/2E Irwin's "effective" surface energy

-YeffY = effective surface energyeff

- 55 -

specimen. This results in a value of Yeff

which is slightly higher than YG calcu-

lated from Gc

2. The large differences between YG and

Y for mortar and concrete are due to the

fact that the surface area A used for

determining Yeff was taken as the nominal

cross-section (2" x 1.25"). This assumes

that the crack propagates in a straight line

through the specimen and does not account for

the new surfaces due to multiplicity of crack

propagation. This phenomena is well docu-

mented in the literature and many studies

have measured the extent of this discrepancy

[33,35,39,48]. No such measurements were

made in this study,

Comparing the different mixes for each method of

measuring the surface energies it can be noted that it

takes four or six times more effective energy Yeff to

fracture the mortar and concrete beams than it does tu

fracture the cement paste beams. This corresponds with

the increased multiplicity of cracks with the increase of

aggregate size. However, measurements of the surface

energy using Irwin's theory do not produce the same

pronounced trend of increasing surface energy with

increasing size of aggregate. This is because the surface

energy is related to the bond paste-aggregate and it is

known that this bond weakens as the size of aggregate

- 56 -

increases [54]. So YG does not increase as markedly for

the three mixes as does Y These values of theeff

fracture mechanics parameters show the same trend as values

published in Reference [46]. Generally the values were

higher but the specimens tested in this study were also

larger. It has been shown [51] that these parameters do

increase with increase of specimen size, and general

accordance can be claimed.

Creep to Rupture Tests

In order to study the gradual yielding of concrete

subjected to high stresses the following procedure was

adopted for each test batch. First, three specimens were

randomly chosen from the batch and tested to determine

their ultimate strength. During these tests load-deforma-

tion data was also recorded. The average value of the

ultimate strengths recorded was then calculated. Load

levels were then defined as fractions of this ultimate

strength. A series of preliminary tests were conducted in

order to determine the appropriate load levels to be used

in this study. The load levels chosen were .80, .85 and

.90 of the ultimate.

The beams were next placed in the previously described

creep to rupture loading devices and subjected to the

- 57 -

desired load levels. Testing was terminated at rupture or

when the desired creep data had been recorded.

The creep behavior as observed in this study is

presented in Figures 11, 12 and 13 for cement paste, mortar

and concrete respectively.*

The following parameters were chosen for comparing the

characteristic behavior of the three mixes used in this

study:

creep rates

magnitude of creep

tertiary creep

deflection at failure

effects of static fatigue on short time tests

Creep Rates: The creep rates recorded for each mix

can be compared in two ways:

a) the rate obtained at each load level as

shown in Figures 11, 12 and 13, and

b) the normalized creep rate, i.e. the creep

rate divided by the corresponding load

level.

Comparing the creep rates at each load level, a fair

degree of uniformity was observed in the resultsr of paste

A detailed presentation of the observed beam deflectionsdata is contained in Appendix B.

** Except when failure occurred,there was no visibledifference in creep rates for .80 and .85 load levels.

- 58 -

Figure 11. Creep to Rupture

3 4 56789710

Time(sec.)

200

175

0×

U.C

IC

C0+J

150

125

100

75

2 34 56789 2 3 4 56789 2 3 4 56789 2 3 4 5 6789 2 3 4 56789 2 3 4 56789 6 2

1 10 10 10 10 10 10

Recordings for Cement Paste

Figure 12. Creep to Rupture

2 3 4 5 61010 10 10 10 10 S710Time(sec.)

200

175

0

C

150

125

100

04-,

u

,ci)ci)

75

10

Recordings for Mortar

Figure 13. Creep to Rupture

200

175

150

125

100

75.

0

1 10 10 10 10" 10' . 10Time (sec.)

q•t0

-

-CUC

c-

o

u4-)U

a,¢)

for Concrete

I

Recordings

specimens tested at any given load level. This trend was

also observed in mortar and concrete specimens tested.

Each mix experienced a sharp increase of creep rate

between the .85 and .90 load levels. The propagation of

microcracks is felt to be the primary mechanism responsible

for the "abrupt" change in creep rate. The growth and

coalescence of the microcracks lead to failure of the

specimens,

Comparing the creep rates of the three mixes, cement

and concrete mixes exhibit, apart from tertiary creep, the

same creep rate for a given load level. The creep rates

for mortar are, however, higher than the other two mixes

for the same load levels. Here it should be remembered

that comparable load levels do not mean the same load is

applied. This is why the second method of comparison is

used.

If the creep rate data were normalized, the creep rate

of paste would be the largest and the creep rates of both

mortar and concrete would be approximately the same. This

may be due to the fact that the mortar and concrete mixes

contained the same amount of aggregate (solid concentra-

tions in the two mixes were the same).

Magnitude of Creep: The magnitude of creep or the

total time-dependent deformation of the beams depended

- 62 -

strongly on two factors:

1) whether or not failure occurred,

2) whether or not creep arrests were

recorded.

Creep arrest is defined as when there is no noticeable

increase of deflection for a period of fifty hours or more.

Figure 11 shows that no creep arrests were recorded

for the cement paste; whereas, for a comparable time

period both mortar and concrete exhibited creep arrests

(see Figures 12 and 13). Also there was a tendency for

earlier creep arrest with increasing aggregate size.

Therefore, the magnitude of creep decreases with increase

of aggregate size.

Tertiary Creep Stage: As mentioned in the fracture

mechanics discussion, the failure of cement paste is

unstable. This fact is confirmed by the near absence of a

tertiary creep stage. Impending failure was not signaled

by an increase of creep rate on the chart recordings. The

two other mixes however showed well defined tertiary creep

stages. The aggregates in these mixes inhibit and arrest

microcrack propagation and through the mechanism of multi-

plicity of cracks, increase the effective surface energy

necessary for failure. Although the tertiary creep stages

of mortar and concrete are much longer than those of paste,

- 63 -

their total duration is still only a matter of seconds.

Thus recognition of impending failure based on

tertiary creep rate data would not provide sufficient time

for corrective action. A more adequate method would

perhaps be based on the time to reach a critical deflec-

tion that must not be exceeded [1].

Deflections at Failure: The unstable nature of

cement paste is evidenced by the scatter of initial and

failure deflections recorded for beams that failed.

The similar scatter in the initial deflections was

recorded for observed tests on concrete beams. However,

the failure deflections for concrete were fairly uniform

and approximately of the same value. This fact would allow

the application of a failure criteria based on reaching a

critical deflection [1].

The deflections at failure for mortar beams were also

fairly uniform; however, they were the highest of the three

materials tested. The range of deflections for the

various load levels employed covers a wider span in the

chart. There seems to be a compromise between the increase

of strength due to the addition of the sand to the cement

paste and the increase of stiffness exhibited by the

beams (the incremental change in strength is larger than

the associated change in stiffness,thus providing larger

- 64 -

initial deformation).

The examination of Figure 12 shows that the mortar

mix exhibits distinct deflections at each load level. More

tests would be needed to comfirm this observation, but if

found true it would then be appropriate to apply the

failure criterion based on the time to reach a critical

deflection that must not be exceeded [1].

Effects of Static Fatigue on Short Time Tests: When

sufficient data was obtained from the long term loading in

the creep to rupture devices, the beams that had not failed

were tested to failure in the Instron Machine.

The load-deflection curves of these tests were then

compared with the twenty-eight day load-deflection curves

of the same batch with emphasis on the following two

points:

1) The failure loads of the beams broken after

long term loading were compared with the"average" failure load at twenty-eight

days.

2) The average slope of the load-deflection

curves taken as the ratio of failure

deflection. The ultimate load was also

compared with that of the specimens tested

at twenty-eight days. This ratio was termed

the "stiffness" of the beams (6/ib) and has

the units (in/lb).

- 65 -

The short term failure loads of the beams after

having been subjected to static load show the following

trends. Both mortar and concrete show approximately the

same increase in strength for each load level. This

increase is approximately 10% for the .85 load level and

5% for the .80 load level. Paste, however, did not show

these trends but showed a slight decrease in strength after

loading. The results of these tests are presented in

Tables 9, 10 and 11 in the form of "final" load levels

(numbers in parentheses). The "final" load level is the

ratio of load at which the creep to rupture test was

performed to final failure load.

The second point of comparison was the stiffness of

the beams before and after the creep to rupture testing.

The deflection per pound of loading (6/lb) was calculated

from the load-deflection curves and compared with the one

obtained from the instantaneous deformation recorded on

the application of the load in creep to rupture. Generally,

the correspondence was good, but variations of up to 20%

from the mean were recorded. The mean values are

2.14 x 10- 4 in/lb for paste, 1.57 x 10- 4 in/lb for mortar

and 1.34 x 10- 4 in/lb for concrete. This confirms the

trend of increased stiffness (lower 6/lb) with increased

size of the aggregate as noted for the unnotched beams

- 66 -

Table 9

Cement Paste Beams Tested

in Creep to Rupture Device with Clock

LoadCast (lbs)

Initial(Final)Load Level

P2 Sept. 7 42.4

P3 Sept. 7 42.4

PA Sept. 7 42.4

PC Aug. 15 43.4

PD Aug. 15 43.4

PB Sept. 7 45.1

P4 Sept. 7 45.1

PD Sept. 7

PD Jul. 31

45.1

48.3

PA Aug. 1 48.3

.80

.80 (.81)

.80 (.81)

.85 (.88)

.85 (.88)

.85

.85 (.84)

.85

.90

.90

204.3

1482

1482

497.5

497

86.5

497

70.3

136

161.3

no

no

no

no

no

yes

no

yes

accidental

accidental

Dates of casting permit differentiation of batches.

- 67 -

Be am

Lengthof test

... (hrs ),..... Failure~~-~~---~ --- ~~~T~-~~--~~~ -~I -- -~- ~~--~ -~-

_ _.___._..____ __. _. ____ ._ __ _ _. _. _ __ __ _~ ____. _.~____.. ____ _~._~__~..._ __~c~-.

Table 10

Mortar Beams Tested

in Creep to Rupture Device with Clock

LoadCast (Ibs)

Initial(Final)Load Level .

MD Jul. 24 68.5

MF Jul. 24 68.5

Ml Nov. 7 70.5

M2 Nov. 7 70.5

M5 Nov. 7 70.5

MB Jul. 29 72.5

MC Jul. 29 72.5

MA Jul. 29 76.5

MB Jul. 24 88.0

.70 (.73)

.70 (.71)

.80 (.76)

.80 (.76)

.80 (.74)

.85 (.68)

.85 (.78)

.90 (.80)

.90

107.2

107

820

840

840

352.5

352.5

353.5120 secs

Dates of casting permit differentiation of batches,

- 68 -

Be am

Lengthof test*(hrs) , . . . Failure

no

no

no

no

no

no

no

no

yes

I ' ' ' -

Table 11

Concrete Beams' Testedin Creep to Rupture Device with Clock

LoadCast (lbs)

Initial(Final)Load Level

C2* Sept. 26

C4* Sept. 26

CF* Sept. 26

CA Aug. 10

65.365.365.371.0

CB Aug. 10 71.0

-CC Aug. 10 71.0

Cl* Sept. 26

CB* Sept. 26

CE* Oct. 18

CF* Oct. 18

CE Jul. 29

CF Jul. 29

69.4

69.465.065.075.175.1

.80 (.74)

.80 (.78)

.80 (.80)

.85

.85 (.75)

.85 (.78)

.85 (.75)

.85 (.77).85 (.71)

.85

.90

.90

1800

1800

1800

.15-(540 secs)

618

562

480

480

1270

226

20 secs

618

* Was initially loaded for one hour on recording. .device.

'Dates of casting permit differentiation of batches.

- 69 -

Beam

Lengthof test(hrs) Failure

no

no

no

yes

no

no

no

no

yes

yes

no

I- -~- -~~-~-~' *-~~"~

(see Table 6). However the increase of stiffness is

higher between mortar and concrete for notched specimens

than the unnotched beams. This may be due to the fact that

relative size of the aggregate as compared to the cross-

section area is more pronounced in the notched beam

than in the unnotched one.

After the long term loading the beams still showed the

same trends of increased stiffness with increase of aggre-

gate size but to a different degree.

The cement paste beams had a general tendency to be

less stiff than the beams tested at twenty-eight days,

which can be explained by the failure mechanism suggested

by Lloyd, Lott and Kesler [16].

This mechanism at a microscopic level is related to

the interaction of the primary and secondary bonds present

in the paste structure. Upon application of load to a

specimen some secondary bonds would tend to fail but the

primary bonds which are at least an order of magnitude

stronger hold the structure together. It is thought that

it is the failure of the secondary bonds that accounts for

the decrease in stiffness and decrease in strength

recorded for the cement paste beams.

The mortar beams showed no trend of increase or

decrease of stiffness after being subjected to static load.

The concrete beams, however, did show a slight increase of

- 70 -

stiffness.

In either case it can be noted that the stiffness of

the beams is weakened by load when compared to the

natural increase of modulus of elasticity with time that

was recorded for the mixes in both tension and compression

(Figures 9 and 10).

Finally when the results of all the tests run in the

creep to rupture devices are tabulated and plotted with

load level vs. time to rupture the following trends are

apparent (see Figures 14, 15 and 16).

No beam failures were recorded for the beams loaded

at an initial load level of .80 for the test times

considered. All failures recorded at the .85 load level

occurred before the sixth decade (12 days).

Apart from accidental failures all failures occurred

in a "triangle" delineated by the .85 load level and a line

from 1.0 load level to the intersection of the sixth

decade and the .85 load level as shown in Figures 14, 15

and 16..

If a linear relationship (on log scale) between time

to failure and load level is assumed, it would take eight

decades or approximately 3.2 years of loading to record all

the failures (if any) at the .8 load level.

Apparently the increase of strength recorded at this

load level (5%) would decrease the probability of failure

- 71 -

1.0

10 102 10410 10 106 ,710

TI M E SEC.

Figure 14. Summary of Tests for Cement Paste.vs. Time to Rupture or Duration of

Load LevelTest.

accidental

X X, vv X(S2 2

--X-- -)( - Xe 3

X Beam Failure

G Init ial Load Level

Final Load Level

.9

.8

.7

o3 10410 10

Figure 15. Summary of Tests forvs. Time to Rupture

06Mortar. Load Levelor Duration of Test.

7I0 7

TIME SEC.

1.0O

-j

w

w

-J

0

-j

.9

.8

.7

10

1.0

10410 1U,O610

Summary of Tests for Concrete. Load Levelvs. Time to Rupture or Duration of Test.

X Beam Failure

o Initial Load Level 2

* Final Load Level

_

_ _

.9

.8S

.7

10

Figure 16.

1 07T I M E SEC.

• A

occurring.

So it can safely be said that the mixes studied here,

and concrete in particular, would not fail under loadings

of up to .80 of the short time ultimate.

This load level is slightly higher than the generally

accepted limit of .70-.75 of the short time ultimate

mentioned by researchers [14,32,33]. An explanation for

this small discrepancy may lie in the following facts.

The ultimate was determined at a slow cross head rate

(.005 in/min). Had it been determined at the higher

cross head rate ASTM allows (.05 in/min) its value may

have been 5% higher. The actual loads at the load levels

tested would represent load levels 5% lower, i.e. .75,

.80 and .85. 1 ,'. -

The beams were in an 'ideal" environment and not

subjected to air drying wi subsequent shrinkage cracks.

It would have been practically impossible to compare the

cement paste beams to the other two mixes if they had been

left to dry in the laboratory environment. This was

attempted but the shrinkage cracks developed in the cement

paste beams generally fractured the specimens.

- 75 -

V. CONCLUSIONS

A series of different experiments were conducted on

cement paste, mortar and concrete beams to study what

role solid inclusions play in the strengthening and

toughening of concrete when subjected to short and long

term loading.

The behavior of these three mixes subjected to long

term loading approaching the ultimate strength indicated

the following trends:

1) Time to failure decreased as the load level

increased.

2) All failures at a load level were recorded

before a certain maximum time for that load

level.

3) There seemed to be a linear relationship

(on a semi log scale) between the maximum

time to failure and the load level tested.

4) The highest load level at which no failures

were recorded was .80 of the short time

ultimate.

5) The total. time dependent deformation

(magnitude of creep) decreased as the size

of aggregate was changed from sand to gravel.

This is believed to be due to the fact that

creep arrests could be achieved sooner with

the larger aggregate size mixes.

- 76 -

6) At comparable load levels the creep rate

was approximately the same for all three

mixes. If normalized to a creep rate per

pound of loading this was no longer true.

7) The effects of long term loading on the

stiffness of the notched beams; cement

paste showed a slight decrease, mortar

showed no noticeable effects and concrete

showed a slight increase of stiffness

compared to that recorded at twenty-eight

days.

- 77 -

REFEREN CES

1. American Society for Testing and Materials (ASTM)Standards, "Definitions Relating to Methods ofTesting," ASTM Designation E 6-61, Sections 64, 65;1961.

2. Tetelman, A.S. and McEvily Jr., AJ., Fracture ofStructural Materials, John Wiley and Sons, Inc.,, NewYork, 19 67.

3. Richards, C.W., Engineering Materials Sciences,Wadsworth Publishing Co., Inc., Belmont, California,1961.

4. Low Jr., J.R., Fracture of Solids, Interscience, NewYork, 1963, pp. 197._-.

5. Garofalo, F., Domis, W. and Gemminger, F., Transactionsof the American Institute of Mining Engineers (AIME)230, 1460; 1964.

6. Garofalo, F., 'Fundamental's of Creep and Creep' 'Rupture,Macmillan, New York, 1965.

7. Cottrell, A.H., The Mechanical Prxoperties of Matter,John Wiley and Sons, Inc., New York, 1964.

8. Moffatt, W.G., Pearsall, G.W. and Wulff, J., TheStructure and Properties of Materials: Vol. I,Structure, John Wiley and Sons, Inc., New York, 1964.

9. Hayden, H.W., Moffatt, W.G. and Wulff, J., TheStructure and Properties of Materials: Vol. III,Mechanical Behavior, John Wiley and Sons, Inc., NewYork, 1965.

10, Broutman, L.J. and Krock, R.H., Modern CompositeMaterials, Addison-Wesley Publishing Co., Reading,Massachusetts, 1967.

11. Curran, R.J., "Dead Load Creep Rupture of Poly MethylMethacrylate," Research Report R63-55, Department ofCivil Engineering, Massachusetts Institute of Tech-nology, December 1963.

- 78 -

12. Nielson, L.E., Mechanical Properties of Polymers,Reinhold Publishing Corp., New York, 1965.

13. Baer, E,, Engineering Design forý Plastics, PolymerScience and Engineering Series (SPFE, ReinholdPublishing Corp., New York, 1964.

14. Winter, G., O'Rourke, C.E., Nilson, A,H. and Urquhart,L.C'., Design of Concrete Structures, McGraw-.Hill, NewYork, 1964'.

15. Neal, J.A., Kung, S.H.C. and Kesler, C.E., "ThirdProgress Report on Mechanism of Fatigue Failure inConcrete," T. & A.M. Report No. 623, University ofIllinois, 1963.

16. Lloyd, J.P., Lott, J.L. and Kesler, C.E ,, "Fatigue ofConcrete," T. & A.M. Report No. 675, University ofIllinois, 1967.

17. Philleo, R.E., "Elastic Properties and Creep ofHardened Concrete," in Concrete and Concrete MakingMaterials, ASTM PublicaITion ST 69-A.

18. Washa, G.W., "Comparison of the Physical and Mechani-cal Properties of Hand-Rodded and Vibrated ConcreteMade with Different Cements," American ConcreteInstitute (ACI) Proceedings, Vol. 36, 1940, pps. 617-648.

19. Troxell, G.E. and Davis, H.E., Composition andProperties of Concrete, McGraw-Hill, New York, 1956.

20. Troxell, G.E., Davis, H.E. and Kelly, J.W., Composi-tion and Properties of Concrete, Second Edition,McGraw-Hill, New York, 1968.

21. Lorman, W.R., "Theory of Concrete Creep," ASTM Pro-ceedings, Vol. 40, 1940, pps. 1082-1102.

22. Hansen, T.C., "Creep of Concrete," Swedish Cement andConcrete Research Institute, Royal Institute of Tech-nology, 1958.

23. Freyssinet, E., "The Deformation of Concrete,"Magazine of Concrete Research, Vol. 3, No. 8, December1951, pps. 49-56.

- 79 -

24. Mullen, W.G. and Dolchi, W.G., "Creep of Portland-Cement Paste," ACI Proceedings, Vol, 64, 1964, pps.1146-1171.

25. Freudenthal, A.M. and Roll, F., "Creep and Creep-Recovery of Concrete Under High Compressive Stress,"Journal of the ACI, June 1968, pps. 1111-1142.

26. Davis, R.E., Davis, H.E. and Brown, E.H., "PlasticFlow and Volume Changes of Concrete," ASTM Proceedings,

......-Vol.- 37, Part II, 1937, pp. 317.

27. Dong, R.G., "A Functional Cumulative Damage Theory andits Relation to two Well-Known Theories," (Palm-Langer-Miner Theory and Williams Theory), Universityof California, January 1967.

28. Glanville, W.H., "The Creep or Flow of Concrete UnderLoad," Building Research Technical Paper No. 12,Department of Scientific and Industrial Research,

_London, 1930.

29. Ross, A.D., "Creep of Concrete Under Variable Stress,"ACI Proceedings, March 1958, pps. 739-758.

30. Fluck, P.G. and Washa, G.W., "Creep of Plain and Rein-forced Concrete," ACI Proceedings, April 1958, pps.879-896.

31. Glanville, W.H. and Thomas, F.G., "Further Investiga-tions on the Creep or Flow of Concrete Under Load,"

--Building--Research Technical Paper No. 21, 1939.

32. Sell, R., "Investigation into Strength of ConcreteUnder Sustained Loads, "_ RILEM Bulletin.No.._5, .1959.

33. Hansen, T.C., "Cracking and Fracture of Concrete and- - ----- ---- Cement Paste," in Causes, Mechanism and Control of

Cracking in Concrete, ACI Publication SP-20, 7198.

.- -. 34. -Leslie, J.R. and Cheesman, W.J., "An Ultrasonic Methodof Studying Deterioration or Cracking in ConcreteStructures," ACI Proceedings, Vol. 46, 1950, pps. 17-36.

35. Shah, S.P. and Chandra, S., "Critical Stress, VolumeChange and Microcracking of Concrete," ACI Proceedings,September 1968, pps. 770-780.

- 80 -

36. Rusch, H., "Physical Problems in Testing Concrete,"Zement-Kolk-Grips, Vol. 12, No. 1, January 1959,Library Transaction No. 86, Cement and ConcreteAssociation, London.

37. Bieniawski, Z.T,, "Mechanisms of Brittle Fracture ofRock," CSIR Report MEG 580, National MechanicalEngineering Research Institute, Pretoria, South Africa,1967.

38. Bieniawski, Z.T., "Mechanisms of Brittle Fracture ofRock": Part III, "Fracture in Tension and Under LongTerm Loading," International Journal of RockMechanics and Mining Sciences, 1967.

39. Kaplan, M.F., "Crack Propagation and Fracture ofConcrete," Journal of the ACI, Vol. 58, No. 5,November 1961, pps. 591-610.

40. ASTM Standards, "Standard Method of Test for SieveAnalysis of Fine and Coarse Aggregates," ASTM Designa-tion C 136.

41. ASTM Standards, "Standard Method of Test forMeasuring Mortar-Making Properties of Fine Aggregate,"ASTM Designation C 87.

42. ASTM Standards, "Standard Method of Test for FlexuralStrength of Concrete Using Simple Beam with Center-Point Loading," ASTM Designation C 293-59. (calcula-tion of the modulus of rupture)

43. ASTM Standards, "Standard Method of Test forCompressive Strength of Molded Concrete Cylinders,"ASTM Designation C 39.

44. Walker, S. and Bloem, D.L., "Effects of Aggregate Sizeon Properties of Concrete," ACI Proceedings, Vol. 57,1960-1961, pps. 283-298.

45. Ishai, 0., "Influence of Sand Concentration and Defor-mations of Mortar Beams Under Low Stress," ACI Pro-ceedings, Vol. 58, No. 5, 1961-1962, pps. 611-623,

46. Moavenzadeh, F., Kuguel, R. and Keat, L.B., "Fractureof Concrete," Research Report R68-5, Department ofCivil Engineering, Massachusetts Institute of Tech-nology, March 15, 1968.

- 81 -

47. Brown Jr., W.F. and Strawley, J.E., Plain StrainCrack Toughness Testing of High Strength MetallicMaterials, ASTM Publication, 1966, (Library ofCongress Catalog Card Number 66-29517)

48. Lott, G.L, and Kesler, C.E., "Crack Propagation inPlain Concrete," T. & A.M. Report No. 648,University of Illinois, 1964.

49. Irwin, G.R.,, Journal of Applied Mechanics, Vol. 61,pp. 49, 1939.

50. Nakayama, T., "Direct Measurement of FractureEnergies of Brittle Heterogeneous Materials," Journalof the American Ceramic Society, 1965.

51. Bremner, T., Unpublished work done at the MaterialsLaboratory, Department of Civil Engineering, Massa-chusetts Institute of Technology, 1968.

52. Hsu, T.T.C., Slate, F.O., Sturman, G.M. and Winter,G., "Microcracking of Plain Concrete and the Shape ofthe Stress-Strain Curve," ACI Proceedings, Vol. 60,1963, pps. 209-224.

53. Glucklich, J., "The Influence of Sustained Loads on theStrength of Concrete," RILEM Bulletin No. 5, December1959, pps. 14-17.

54. Hughes, B.P. and Chapman, G.P., "The Deformation ofConcrete and Microcracking in Compression or Tensionwith Particular Reference to Aggregate Size," Magazineof Concrete Research, Vol. 18, No. 54, March 1966, pps.19-24.

55. Welch, G.B., "Tensile Strains in Unreinforced ConcreteBeams," Magazine of Concrete Research, Vol. 18, No. 54,March 1966.

- 82 -

Appendix A

List of Abbreviations in Text

(in alphabetic order)

A aggregate

a notch depth (inches)

C concrete

c cement

cm centimeter (0.01 meter)

d beam depth (inches)

E modulus of elasticity

ft foot (12 inches)

g gram (.001 kilo)

G critical strain energy release rate

(in * lb/in2 )

in inch

K critical stress intensity factor

(lb * in- 3/2)

L length of beam (inches)

lb pound

M mortar

P paste (cement)

PMMA poly methyl methacrylate (polymer)

psi pounds per square inch (ib/in2 )

one-half of grain diameter

S span of testing (inches)

S-N stress vs. number of cycles (fatigue)

SSD saturated surface dry

T time

- 83 -

t service life

TM absolute melting temperature (oK)

V creep rate

W water

w beam width (inches)

Yeff effective surface energy

YG specific surface energy calculated fromIrwin's expression

rK 2/2E

6deflection of beam

6/lb deflection per pound of loading (in/lb)

measure of stiffness of notched beams

Sstrain

a stress (ib/in2 )

- 84 -

Appendix B

List of Deflections

Recorded in Creep to Rupture Curves

(Figures 11,

PE*

Sept. 7

12, 13)

PF* PC*

Sept. 7 Jul. 31 Jul. 31

Load (ibs)

Load Level

InitialDeflection

7 secs

15 secs

47.7

.90

98

47,7

.90

86

3 secs 6 secs104 93

48.3

.90

106

113

12 secs 116

60 secs

900 secs

48.3.90

117

126

25 secs135

41 secs 30 secs120

47 secs125

138

36000 secs

360000 secs

* Beam failed under this load.

- 85 -

Be am

Cast

PF

Jul. 31

48.3.90

98105

109

111

115

128

104000133

_ __ _____ ~_ L

- -I- -- I- --

PE* PD*

Aug. 13 Sept. 7

P4 PB

Sept. 7 Nov. 19

Load (ibs)

Load Level

InitialDeflection

7 sees

15 sees

60 sees

900 sees

36000 sees

360000 sees

43.4

.85

116124

127

131

137

158

580000178

* Beam failed under this load.

- 86 -

Be am

Cast

45.1.85

49.0

.8545.1

.85

100

103

104

107

69 sees109

101

108

129

102

106

120

670000135

1120000126

--- --- -- · I --- ·~-C~--Cur~-~·-C--*-·CC-- -- ~I-I· Y-Cr.C-CI-)-·UI·--r~f-·_.

i · ~ ~· · ~·~ L -~ ·

Beam

Cast

Load (lbs)

Load Level

InitialDeflection

7 sees15 sees

60 sees

900 sees

36000 sees

360000 sees

PB

Aug. 15

PE

Nov. 21

PC

Aug. 1

43.0

.80

93103

o106110

116

40.8

.80

48.0

.80

95

98

99

101

1065820

112

78

82

83

84

88

94

324000133

100

- 87 -

L~ ' ' -- · - -- L-··~---·----- --

- - - ~ ~--1L -- L~--~ L---

Beam MF*

Jul. 24 Jul. 24 Aug. 5 Aug. 5 Aug. 5

Load (ibs)

Load Level

InitialDeflection

7 secs

15 secs

60 secs

900 secs

36000 secs

360000 secs

88.0

.90

135

154

156

61 secs166

75 secs178

88.0

.90

132

144

148

155

393 secs166

456183

68.7

.85

123

126

133

138

146

113000 160000149 142

* Beam failed under this load.

- 88 -

Cast

68.7

.85

64.0

.80

118123

128

137

139

118

122

127

132

140

174000143

---C-*-rfC----CCCCCICt - -____._,_~.~_~. _~-C--·-C~I~

- - --- · · -- C - -. - · _ - · --

MD* MA MB MC

MC M2

Nov.. 7 Nov. 7

M5 MC

Nov, 7 Aug. 5Retest

Load (ibs)

Load Level

InitialDeflection

7 secs

15 secs

60 secs

900 secs

36000 sees

360000 sees

70.5.80

90

9597

102

111

128

540000129

720000130

1240000130

70.5.80

104

108

110

114

121

70.5

.80 .85 (.82)46 days

8892

96

103

3000 3600124 105

8400 6300126 107

continued onother loadingframe

- 89 -

Be am

Cast

78.0

126

132

134

139

148

170

900000193

1113000193

· _ _· __ _ _.··_L·l ·

_ · · _ · · · _ _ ~~~

Beam CE* C5 c6* CC* C5K*

Sept. 26 Sept. 26 Oct. 18 Oct. 18 Oct. 18

Load (ibs)

Load Level

InitialDeflection

7 sees

15 sees

60 sees

900 sees

36000 sees

360000 sees

73.5.90

101

109

114

23 sees120

29 sees130

73.5.90 (.83)

98

103

106

109

118

129

54000130

64800130

69.0

.90

69.0

.90

90

94

96

102

240 sees108

480112

1200118

1375132

106

2280112

2450130

69.0

.90

106

112

115

122

90 sees125

105 sees134

* Beam failed under this load.

- 90 -

Cast

1 -- · - -· - - · 'L· · - -- - --- I-· - - - - -P-

- · -· --

CA*

Sept. 26

C6*Sept. 26

Cl

Sept. 26

Load (ibs)

Load Level

InitialDeflection

7 secs

15 secs

60 secs

900 secs

36000 secs

360000secs

66.5

.85 (.76)

100

102

69.4

.85

98100

102

106

300 secs112

480 secs120

525 secs128

720000107

1200000107

* Beam failed under this load.

- 91 -

Beam

Cast

C3

Oct. 18

69.4

.85

100

103

50 secs112

64 secs124

69.4

.85

100

101

102

106

107

144000110

___~____ ___ __ _ _ _ I___ 1 _ _~II_~_____ _________~ ____ ____II____~_ _C ___

C · · __ _ __ _ II_ · _ LI _I

C5 CA

Sept. 26 Oct. 13. . . . . . . . . .R et e s.t . . . . . .

Load (ibs)

Load Level

InitialDeflection

7 secs

15 secs

60 secs

900 sees

36000 secs

360000 sees

.85 (.78)61.1

.80 (.76)

98

101

104

106

180000110

198000111

306000111

92

100

415000105

505000107

-92 -

Beam

Cast

~___ _ · · · _ .._ · · _·~~_~_·_ _ _I · __ ·

- · ·